Unoccupied adsorption sites

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

In this equation, Aads f corresponds to the enthalpy difference between occupied and unoccupied adsorption sites and contains Meads-s be difference of the solvation enthalpies of Meads and S. Asub is the sublimation enthalpy, which is related to the interaction enthalpy per Me bond, Hle-Me, approximated as y/i in the case of first nearest neighbors (cf. eqs. 2.2 and 2.3). The terms and Vads represent the mean vibrational volumes of an atom in a kink site position or in an adatom position, respectively [3.269]. They are related to the mean atomic vibration frequencies in the 3D Me bulk lattice and in the Meads overlayer, respectively. 

Under electrochemical conditions and T, P = constant, adsorption isotherms can be derived using standard statistical considerations to calculate the Gibbs energy of the adsorbate in the interphase and the equilibrium condition for the electrochemical potentials of the adsorbed species i in the electrolyte and in the adsorbed state (eq. (8.15) in Section 8.2). A model for the statistical considerations consists of a 2D lattice of arbitrary geometry with Ns adsorption sites per unit area. In the case of a 1/1 adsorption, each adsorbed particle can occupy only one adsorption site so that the maximal number of adsorbed particles per unit area in the compact monolayer is determined by A ax = Ng. Then, this model corresponds to the simple Ising model. The number of adsorbed particles, A ads< and the number of unoccupied adsorption sites, No, per unit area are given by... 

Adsorption rates. The most common assumption for adsorption and desorption rates is that used by Langmuir in the derivation of his isotherm equation [20]. These are proportionality of the adsorption rate to the partial pressure or concentration of the species and the number of still unoccupied adsorption sites and of the desorption rate to the number of sites occupied by the respective species. This is as for a reversible reaction of the species with an unoccupied site ... 

Adsorption and desorption rates are usually taken as postulated by Langmuir, that is, as for a reversible reaction of the molecule in the fluid phase with an unoccupied adsorption site. 

Because of its simplicity and wide utility, the Langmuir isotherm has found wide applicability in a number of useful situations. Like many such classic approaches, it has its fundamental weaknesses, but its utility generally outweighs its shortcomings. The Langmuir isotherm model is based on the assumptions that adsorption is restricted to monolayer coverage, that adsorption is localized (i.e., that specific adsorption sites exist and interactions are between the site and a specific molecule), and that the heat of adsorption is independent of the amount of material adsorbed. The Langmuir approach is based on a molecular kinetic model of the adsorption-desorption process in which the rate of adsorption (rate constant /ca) is assumed to be proportional to the partial pressure of the adsorbate (p) and the number of unoccupied adsorption sites (N - n), where N is the total number of adsorption sites on the surface and n is the number of occupied sites, and the rate of desorption (rate constant d) is proportional to n. 

To describe the competitive adsorption of two compounds (A and B) under isothermal conditions, an additive Langmnir model can be used. The adsorption rate of A molecules (r ) depends on partial pressure and a nnmber of unoccupied adsorption sites (1 -0 -65) ... 

We can think of a heterogeneous catalyst as a collection of active sites (denoted by ) located at a surface. The total number of sites is constant and equal to N (if there is any chance of confusion with N atoms, we will use the symbol N ). The adsorption of the reactant is formally a reaction with an empty site to give an intermediate I (or more conveniently R if we explicitly want to express that it is the reactant R sitting on an adsorption site). All sites are equivalent and each can be occupied by a single species only. We will use the symbol 6r to indicate the fraction of occupied sites occupied by species R, making N6r the number of occupied sites. Hence, the fraction of unoccupied sites available for reaction will be 1 - 0r The following equations represent the catalytic cycle of Fig. 2.7 ... 

In many cases the number of occupied adsorption sites is not equivalent to the number of unit cells. Often, repulsive interactions bet veen adsorbed species prevents filling of all sites and adsorption may only be possible if all neighboring sites are unoccupied. Adsorbate structures are described according to hoiv the neiv unit cell of adsorbate and substrate relate to the original unit cell of the substrate. Figure 5.7 shows a few examples along with the nomenclature used. 

However, it is questionable whether a particle which is coated with an absorbing liquid film will have any unoccupied active sites for adsorption to occur. It may be preferable to use either the absorption or adsorption model but not both additively. 

All the above mechanisms can be called the simplest catalytic oscillators. In all these mechanisms self-oscillations of the reaction rate are realized due to the combination of the fast system of steps (adsorption mechanism) leading to the sharp change in the number of unoccupied surface sites and of the "slow reversible step ensuring self-oscillations of their concentration. If the parameters of the "buffer step are sufficiently small compared with those of the main mechanism, all these oscillations will be typically relaxa-tional. 

In order for a molecule to ultimately adsorb, it must first collide with the surface with sufficient energy to overcome any activation barrier, indicated as in Figure 5.9. The Ea can be negligibly small, as in physisorption, or can be significant, as in the case of chemical reactions. The rate at which adsorption proceeds will depend on an adsorption rate constant k, on the concentration or partial pressure of the adsorbing species (p), and on the fraction of adsorption sites that are unoccupied. Thus, we can express die adsorption rate as... 

For instance, an adatom site ads on the surface is transferred to an unoccupied or free" adsorption site after dissolution. A surface atom" site is changed to a vacant site vac on the surface, accordingly. In both cases each single ion transfer changes the number of sites on the surface by unity ... 

Given in Table 10.7 are the surface reactions and corresponding activity adsorption isotherm model equations used in MINTEQA2 as presented by Allison et al. (1991). In these expressions SOH and SOH M represent unoccupied surface sites and surface sites occupied by species M. Because the and Freundlich isotherm models assume an infinite number of available sorption sites, the con-... 

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